結果

問題 No.1889 K Consecutive Ks (Hard)
ユーザー miscalcmiscalc
提出日時 2022-03-18 19:42:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,287 ms / 6,000 ms
コード長 5,277 bytes
コンパイル時間 226 ms
コンパイル使用メモリ 82,380 KB
実行使用メモリ 253,284 KB
最終ジャッジ日時 2024-10-04 07:33:27
合計ジャッジ時間 30,655 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 37 ms
54,580 KB
testcase_01 AC 35 ms
53,132 KB
testcase_02 AC 2,260 ms
252,944 KB
testcase_03 AC 35 ms
54,168 KB
testcase_04 AC 33 ms
53,968 KB
testcase_05 AC 33 ms
54,516 KB
testcase_06 AC 33 ms
53,272 KB
testcase_07 AC 37 ms
60,044 KB
testcase_08 AC 36 ms
59,192 KB
testcase_09 AC 2,267 ms
249,128 KB
testcase_10 AC 2,287 ms
252,400 KB
testcase_11 AC 593 ms
110,276 KB
testcase_12 AC 1,149 ms
148,460 KB
testcase_13 AC 663 ms
121,084 KB
testcase_14 AC 1,301 ms
155,820 KB
testcase_15 AC 1,211 ms
170,148 KB
testcase_16 AC 2,264 ms
248,660 KB
testcase_17 AC 607 ms
112,804 KB
testcase_18 AC 2,227 ms
246,200 KB
testcase_19 AC 2,216 ms
250,880 KB
testcase_20 AC 2,236 ms
253,284 KB
testcase_21 AC 2,258 ms
252,168 KB
testcase_22 AC 2,228 ms
253,160 KB
testcase_23 AC 1,190 ms
163,736 KB
testcase_24 AC 2,267 ms
253,196 KB
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ソースコード

diff # 

# https://judge.yosupo.jp/submission/55648

# AtCoder Libary v1.4 を python に移植したもの
# https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
 
MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
rate2 = [0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0]
irate2 = [0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0]
rate3 = [0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0]
irate3 = [0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0]
 
def butterfly_base4(a):
  n = len(a)
  h = (n - 1).bit_length()
  le = 0
  while le < h:
    if h - le == 1:
      p = 1 << (h - le - 1)
      rot = 1
      for s in range(1 << le):
        offset = s << (h - le)
        for i in range(p):
          l = a[i + offset]
          r = a[i + offset + p] * rot
          a[i + offset] = (l + r) % MOD
          a[i + offset + p] = (l - r) % MOD
        rot *= rate2[(~s & -~s).bit_length()]
        rot %= MOD
      le += 1
    else:
      p = 1 << (h - le - 2)
      rot = 1
      for s in range(1 << le):
        rot2 = rot * rot % MOD
        rot3 = rot2 * rot % MOD
        offset = s << (h - le)
        for i in range(p):
          a0 = a[i + offset]
          a1 = a[i + offset + p] * rot
          a2 = a[i + offset + p * 2] * rot2
          a3 = a[i + offset + p * 3] * rot3
          a1na3imag = (a1 - a3) % MOD * IMAG
          a[i + offset] = (a0 + a2 + a1 + a3) % MOD
          a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
          a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
          a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
        rot *= rate3[(~s & -~s).bit_length()]
        rot %= MOD
      le += 2
 
def butterfly_inv_base4(a):
  n = len(a)
  h = (n - 1).bit_length()
  le = h
  while le:
    if le == 1:
      p = 1 << (h - le)
      irot = 1
      for s in range(1 << (le - 1)):
        offset = s << (h - le + 1)
        for i in range(p):
          l = a[i + offset]
          r = a[i + offset + p]
          a[i + offset] = (l + r) % MOD
          a[i + offset + p] = (l - r) * irot % MOD
        irot *= irate2[(~s & -~s).bit_length()]
        irot %= MOD
      le -= 1
    else:
      p = 1 << (h - le)
      irot = 1
      for s in range(1 << (le - 2)):
        irot2 = irot * irot % MOD
        irot3 = irot2 * irot % MOD
        offset = s << (h - le + 2)
        for i in range(p):
          a0 = a[i + offset]
          a1 = a[i + offset + p]
          a2 = a[i + offset + p * 2]
          a3 = a[i + offset + p * 3]
          a2na3iimag = (a2 - a3) * IIMAG % MOD
          a[i + offset] = (a0 + a1 + a2 + a3) % MOD
          a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
          a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
          a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
        irot *= irate3[(~s & -~s).bit_length()]
        irot %= MOD
      le -= 2
 
def multiply(s, t):
  n = len(s)
  m = len(t)
  if min(n, m) <= 60:
    a = [0] * (n + m - 1)
    for i in range(n):
      if i % 8 == 0:        
        for j in range(m):
          a[i + j] += s[i] * t[j]
          a[i + j] %= MOD
      else:
        for j in range(m):
          a[i + j] += s[i] * t[j]
    return a.copy()
  a = s.copy()
  b = t.copy()
  z = 1 << (n + m - 2).bit_length()
  a += [0] * (z - n)
  b += [0] * (z - m)
  butterfly_base4(a)
  butterfly_base4(b)
  for i in range(z):
    a[i] *= b[i]
    a[i] %= MOD
  butterfly_inv_base4(a)
  a = a[:n + m - 1]
  iz = pow(z, MOD - 2, MOD)
  return [v * iz for v in a]

n, m = map(int, input().split())

d = [0] * (n + 10)
for i in range(2, m + 1):
  k = 1
  while k * i <= n:
    d[k * i - 1] += 1
    k += 1

pw = [0] * (n + 10)
pw[1], pw[2] = 1, m - 2
for i in range(2, n):
  pw[i + 1] = (m - 1) * pw[i] % MOD

dp1 = [0] * (n + 10)
dp2 = [1] * (n + 10)
for i in range(n):
  dp2[i + 1] = (m - 1) * dp2[i] % MOD

def onlineconvolution(l, r):
  if r - l <= 30:
    for i in range(l, r):
      for j in range(l, i):
        dp1[i] += dp2[j] * d[i - j]
        dp1[i] %= MOD
      for j in range(l, i):
        dp2[i] -= dp1[j] * pw[i - j]
        dp2[i] %= MOD
    return
  c = (l + r) // 2
  onlineconvolution(l, c)
  dp20 = dp2[l : c]
  d0 = d[: r - l]
  r1 = multiply(dp20, d0)
  for i in range(c, r):
    dp1[i] += r1[i - l]
    dp1[i] %= MOD
  dp10 = dp1[l : c]
  pw0 = pw[: r - l]
  r2 = multiply(dp10, pw0)
  for i in range(c, r):
    dp2[i] -= r2[i - l]
    dp2[i] %= MOD
  onlineconvolution(c, r)

onlineconvolution(0, n + 1)
ans = (pow(m, n, MOD) - dp2[n]) % MOD
print(ans)
0